Finite Group Databasebeta

← C5×D33⋊D57 #49178708

Subgroups — C5×D33⋊D57 #49178708

Order 37620.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C19×D33C211yesmaximal, characteristic, complemented
2C3×C5×D627C211yesmaximal, characteristic, complemented
3C5×C11×C3⋊D57C211yesmaximal, characteristic, complemented
4C5×D33⋊D19—31nomaximal
5C5×D11×D57—31nomaximal
6C32×C5×C11×C19C2211yescharacteristic, complemented, Hall
7D33⋊D57C511yesmaximal, characteristic, direct product factor, Hall
8C5×D627D311yescharacteristic, complemented
9C5×C19×D33D311yescharacteristic, complemented
10C5×C11×D57—31no—
11C5×C11×D57—31no—
12C5×C11×D57—61no—
13C3×C5×D209—31no—
14C3×C5×C19×D11—31no—
15C5×D11×D19—91noHall
16C11×C3⋊D57C2×C511yescharacteristic, complemented
17C3×D627C2×C511yescharacteristic, complemented
18C3×C19×D33C2×C511yescharacteristic, complemented
19C5×D3×D57—111nomaximal, Hall
20C3×C5×C11×C19—21no—
21C3×C5×C11×C19C2×D311yescharacteristic, complemented
22C3×C5×C11×C19C2×D311yescharacteristic, complemented
23D33⋊D19—31no—
24D11×D57—31no—
25C5×D209—31no—
26C5×C19×D11—31no—
27C5×C11×D19—91no—
28C5×(C3⋊D3)⋊D11—191nomaximal, Hall
29C32×C11×C19C22×C511yescharacteristic, complemented, Hall
30C5×C3⋊D57D1111yescharacteristic, complemented
31C3×C5×D57—111no—
32C3×C5×D3×C19—111no—
33D627C5×D311yescharacteristic, complemented
34C19×D33C5×D311yescharacteristic, complemented
35C11×D57—31no—
36C11×D57—31no—
37C11×D57—61no—
38C3×D209—31no—
39C3×C19×D11—31no—
40C2×C5×D57—331no—
41C5×D3×D19—331no—
42C5×C11×C19D3211yescharacteristic, complemented, Hall
43C5×C11×C3⋊D3—191no—
44C3×C5×D33—191no—
45C3×C5×D33D1911yescharacteristic, complemented
46C32×C5×C19C2×D1111yescharacteristic, complemented, Hall
47D11×D19—91noHall
48D3×D57—111noHall
49C5×D3×D11—571no—
50C5×D3×D11—571no—
51C3×C11×C19—21no—
52C3×C11×C19C2×C5×D311yescharacteristic, complemented
53C3×C11×C19C2×C5×D311yescharacteristic, complemented
54C2×C3×C5×C19—331no—
55C5×D57—31no—
56C5×D57—31no—
57C5×D57—61no—
58C5×D57—111no—
59C5×D3×C19—111no—
60C3×C5×D19—331no—
61C32×C5×C11C2×D1911yescharacteristic, complemented, Hall
62D209—31no—
63C11×D19—91no—
64C19×D11—31no—
65(C3⋊D3)⋊D11—191noHall
66C2×C5×D19—991noHall
67C3⋊D57C5×D1111yescharacteristic, complemented
68C3×D57—111no—
69C3×D3×C19—111no—
70C5×D33—191no—
71C5×D33D5711yescharacteristic, complemented
72C5×D3×C11—571no—
73C5×D3×C11—571no—
74C5×D3×C11—1141no—
75C3×C5×D11—31no—
76C3×C5×D11—571no—
77C3×C5×C19—21no—
78C3×C5×C19D3×D1111yescharacteristic, complemented
79C3×C5×C19D3×D1111yescharacteristic, complemented
80C2×D57—331no—
81D3×D19—331no—
82C2×C5×D11—1711noHall
83C11×C19C5×D3211yescharacteristic, complemented, Hall
84C11×C3⋊D3—191no—
85C3×D33—191no—
86C3×D33C5×D1911yescharacteristic, complemented
87C2×C5×C19—331no—
88C5×D19—91no—
89C5×D19—331no—
90C5×D32—2091noHall
91C32×C19C2×C5×D1111yescharacteristic, complemented, Hall
92C3×C5×C11—21no—
93C3×C5×C11D3×D1911yescharacteristic, complemented
94C3×C5×C11C2×D5711yescharacteristic, complemented
95D3×D11—571no—
96D3×D11—571no—
97C2×C3×C19—331no—
98D57—31no—
99D57—31no—
100D57—61no—
101D57—111no—
102C3×D19—331no—
103D3×C19—111no—
104C2×C5×C11—1711no—
105C5×D11—31no—
106C5×D11—571no—
107C32×C11C2×C5×D1911yescharacteristic, complemented, Hall
108C5×C19(C3⋊D3)⋊D1111yescharacteristic, complemented, Hall
109C5×C3⋊D3—191no—
110C3×C5×D3—111no—
111C3×C5×D3—2091no—
112C2×D19—991noHall
113D33—191no—
114D33C5×D5711yescharacteristic, complemented
115C3×D11—31no—
116C3×D11—571no—
117D3×C11—571no—
118D3×C11—571no—
119D3×C11—1141no—
120C2×C5×D3—6271no—
121C2×C5×D3—6271no—
122C3×C19—21no—
123C3×C19C5×D3×D1111yescharacteristic, complemented
124C3×C19C5×D3×D1111yescharacteristic, complemented
125C5×C11D3×D5711yescharacteristic, complemented, Hall
126C32×C5D11×D1911yescharacteristic, complemented, Hall
127C2×D11—1711noHall
128C2×C19—331no—
129D19—91no—
130D19—331no—
131D32—2091noHall
132C3×C11—21no—
133C3×C11C5×D3×D1911yescharacteristic, complemented
134C3×C11C2×C5×D5711yescharacteristic, complemented
135C2×C3×C5—331no—
136C2×C3×C5—6271no—
137C5×D3—111no—
138C5×D3—571no—
139C5×D3—571no—
140C5×D3—1141no—
141C5×D3—2091no—
142C2×C11—1711no—
143D11—31no—
144D11—571no—
145C22×C5—18811noHall
146C19C5×(C3⋊D3)⋊D1111yescharacteristic, complemented, Sylow
147C3⋊D3—191no—
148C3×D3—111no—
149C3×D3—2091no—
150C3×C5—21no—
151C3×C5D11×D5711yescharacteristic, complemented
152C3×C5D33⋊D1911yescharacteristic, complemented
153C2×D3—6271no—
154C2×D3—6271no—
155C11C5×D3×D5711yescharacteristic, complemented, Sylow
156C2×C5—331no—
157C2×C5—6271no—
158C2×C5—1711no—
159C32C5×D11×D1911yescharacteristic, complemented, Sylow
160C2×C3—331no—
161C2×C3—6271no—
162D3—111no—
163D3—571no—
164D3—571no—
165D3—1141no—
166D3—2091no—
167C5D33⋊D5711yescharacteristic, direct product factor, Sylow
168C22—18811noSylow
169C3—21no—
170C3C5×D11×D5711yescharacteristic, complemented
171C3C5×D33⋊D1911yescharacteristic, complemented
172C2—331no—
173C2—6271no—
174C2—1711no—
subgroupG/H
center, hypercenterC5D33⋊D57
commutator, cosocle, hypocenterC32×C11×C19C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C32×C11×C19
UCSC1 ◁ C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×C19×D33C2semidirect
2. C3×C5×D627C2semidirect
3. C5×C11×C3⋊D57C2semidirect
6. C32×C5×C11×C19C22semidirect
7. D33⋊D57C5direct (N × H)
8. C5×D627D3semidirect
9. C5×C19×D33D3semidirect
16. C11×C3⋊D57C2×C5semidirect
17. C3×D627C2×C5semidirect
18. C3×C19×D33C2×C5semidirect
21. C3×C5×C11×C19C2×D3semidirect
22. C3×C5×C11×C19C2×D3semidirect
29. C32×C11×C19C22×C5semidirect
30. C5×C3⋊D57D11semidirect
33. D627C5×D3semidirect
34. C19×D33C5×D3semidirect
42. C5×C11×C19D32semidirect
45. C3×C5×D33D19semidirect
46. C32×C5×C19C2×D11semidirect
52. C3×C11×C19C2×C5×D3semidirect
53. C3×C11×C19C2×C5×D3semidirect
61. C32×C5×C11C2×D19semidirect
67. C3⋊D57C5×D11semidirect
71. C5×D33D57semidirect
78. C3×C5×C19D3×D11semidirect
79. C3×C5×C19D3×D11semidirect
83. C11×C19C5×D32semidirect
86. C3×D33C5×D19semidirect
91. C32×C19C2×C5×D11semidirect
93. C3×C5×C11D3×D19semidirect
94. C3×C5×C11C2×D57semidirect
107. C32×C11C2×C5×D19semidirect
108. C5×C19(C3⋊D3)⋊D11semidirect
114. D33C5×D57semidirect
123. C3×C19C5×D3×D11semidirect
124. C3×C19C5×D3×D11semidirect
125. C5×C11D3×D57semidirect
126. C32×C5D11×D19semidirect
133. C3×C11C5×D3×D19semidirect
134. C3×C11C2×C5×D57semidirect
146. C19C5×(C3⋊D3)⋊D11semidirect
151. C3×C5D11×D57semidirect
152. C3×C5D33⋊D19semidirect
155. C11C5×D3×D57semidirect
159. C32C5×D11×D19semidirect
167. C5D33⋊D57direct (N × H)
170. C3C5×D11×D57semidirect
171. C3C5×D33⋊D19semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×C19×D332
C3×C5×D6272
C5×C11×C3⋊D572
C5×D33⋊D193
C5×D11×D573
D33⋊D575
C5×D3×D5711
C5×(C3⋊D3)⋊D1119